If tan x = 3/5 and tan y = 1/4, then show that x+y = pi/4.
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tan x =3/5, tan y = 1/4
tan (x+y)= (tan x + tan y)/ (1- tan x tan y)
= (3/5+1/4)/(1-3/5*1/4)
= [(12+5)/20÷(20-3)/20]
=[17/20÷17/20]
=1
tan (x+y) = tan 45
= tan pi/4
therefore
x+y = pi/4
tan (x+y)= (tan x + tan y)/ (1- tan x tan y)
= (3/5+1/4)/(1-3/5*1/4)
= [(12+5)/20÷(20-3)/20]
=[17/20÷17/20]
=1
tan (x+y) = tan 45
= tan pi/4
therefore
x+y = pi/4
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